Project 1: The Game of Hog

5-sided die

I know! I'll use my
Higher-order functions to
Order higher rolls.

Introduction

Important submission note: For full credit:

  • Submit with Phase 1 complete by Tuesday, Feb 7, worth 1 pt.
  • Submit the complete project by Friday, Feb 10.

Try to attempt the problems in order, as some later problems will depend on earlier problems in their implementation and therefore also when running ok tests.

You may complete the project with a partner.

You can get 1 bonus point by submitting the entire project by Thursday, Feb 9 You can receive extensions on the project deadline and checkpoint deadline, but not on the early deadline, unless you're a DSP student with an accommodation for assignment extensions.

In this project, you will develop a simulator and multiple strategies for the dice game Hog. You will need to use control statements and higher-order functions together, as described in Sections 1.2 through 1.6 of Composing Programs, the online textbook.

When students in the past have tried to implement the functions without thoroughly reading the problem description, they’ve often run into issues. 😱 Read each description thoroughly before starting to code.

Rules

In Hog, two players alternate turns trying to be the first to end a turn with at least GOAL total points, where GOAL defaults to 100. On each turn, the current player chooses some number of dice to roll, up to 10. That player's score for the turn is the sum of the dice outcomes. However, a player who rolls too many dice risks:

  • Sow Sad. If any of the dice outcomes is a 1, the current player's score for the turn is 1.
  • Example 1: The current player rolls 7 dice, 5 of which are 1's. They score 1 point for the turn.
  • Example 2: The current player rolls 4 dice, all of which are 3's. Since Sow Sad did not occur, they score 12 points for the turn.

In a normal game of Hog, those are all the rules. To spice up the game, we'll include some special rules:

  • Pig Tail. A player who chooses to roll zero dice scores 2 * abs(tens - ones) + 1 points; where tens, ones are the tens and ones digits of the opponent's score. The ones digit refers to the rightmost digit and the tens digit refers to the second-rightmost digit.
  • Example 1:

    • The opponent has 46 points, and the current player chooses to roll zero dice. 2 * abs(4 - 6) + 1 = 5, so the player gains 5 points.
  • Example 2:

    • The opponent has 73 points, and the current player chooses to roll zero dice. 2 * abs(7 - 3) + 1 = 9.
  • Square Swine. After a player gains points for their turn, if the resulting score is a perfect square, then increase their score to the next higher perfect square. A perfect square is any integer n where n = d * d for some integer d.
  • Example 1:

    • A player has 12 points and rolls 3 dice that total 13 points. Their new score would be 25, but since 25 is 5 squared, their score is increased to 6 squared: 36.
  • Example 2:

    • A player has 12 points and rolls 3 dice that total 12 point. Their new score would be 24, which is not a perfect square.
  • Example 3:

    • A player has 0 points and rolls 5 dice, but one is a 1, so their new score would be 1. 1 is a perfect square, and so their score is increased to 4.
  • Example 4:

    • A player has 80 points and rolls 10 dice, but three are 1's, so their new score would be 1. 81 is 9 squared, so their new score is 10 squared: 100. They win the game.

Download starter files

To get started, download all of the project code as a zip archive. Below is a list of all the files you will see in the archive once unzipped. For the project, you'll only be making changes to hog.py.

  • hog.py: A starter implementation of Hog
  • dice.py: Functions for making and rolling dice
  • hog_gui.py: A graphical user interface (GUI) for Hog (updated)
  • ucb.py: Utility functions for CS 61A
  • hog_ui.py: A text-based user interface (UI) for Hog
  • ok: CS 61A autograder
  • tests: A directory of tests used by ok
  • gui_files: A directory of various things used by the web GUI

You may notice some files other than the ones listed above too—those are needed for making the autograder and portions of the GUI work. Please do not modify any files other than hog.py.

Logistics

The project is worth 25 points, of which 1 point is for submitting Phase 1 by the checkpoint date of Tuesday, Feb 7.

You will turn in the following files:

  • hog.py

You do not need to modify or turn in any other files to complete the project. To submit the project, submit the required files to the appropriate Gradescope assignment.

For the functions that we ask you to complete, there may be some initial code that we provide. If you would rather not use that code, feel free to delete it and start from scratch. You may also add new function definitions as you see fit.

However, please do not modify any other functions or edit any files not listed above. Doing so may result in your code failing our autograder tests. Also, please do not change any function signatures (names, argument order, or number of arguments).

Throughout this project, you should be testing the correctness of your code. It is good practice to test often, so that it is easy to isolate any problems. However, you should not be testing too often, to allow yourself time to think through problems.

We have provided an autograder called ok to help you with testing your code and tracking your progress. The first time you run the autograder, you will be asked to log in with your Ok account using your web browser. Please do so. Each time you run ok, it will back up your work and progress on our servers.

The primary purpose of ok is to test your implementations.

If you want to test your code interactively, you can run
 python3 ok -q [question number] -i 
with the appropriate question number (e.g. 01) inserted. This will run the tests for that question until the first one you failed, then give you a chance to test the functions you wrote interactively.

You can also use the debugging print feature in OK by writing

 print("DEBUG:", x) 
which will produce an output in your terminal without causing OK tests to fail with extra output.

Graphical User Interface

A graphical user interface (GUI, for short) is provided for you. At the moment, it doesn't work because you haven't implemented the game logic. Once you complete the play function, you will be able to play a fully interactive version of Hog!

Once you've done that, you can run the GUI from your terminal:

python3 hog_gui.py

Getting Started Videos

These videos may provide some helpful direction for tackling the coding problems on this assignment.

To see these videos, you should be logged into your berkeley.edu email.

YouTube link

Phase 1: Rules of the Game

In the first phase, you will develop a simulator for the game of Hog.

Problem 0 (0 pt)

The dice.py file represents dice using non-pure zero-argument functions. These functions are non-pure because they may have different return values each time they are called, and so a side-effect of calling the function may be changing what will happen when the function is called again. The documentation of dice.py describes the two different types of dice used in the project:

  • Fair dice produce each possible outcome with equal probability. The four_sided and six_sided functions are examples.
  • Test dice are deterministic: they always cycle through a fixed sequence of values that are passed as arguments. Test dice are generated by the make_test_dice function.

Before writing any code, read over the dice.py file and check your understanding by unlocking the following tests.

python3 ok -q 00 -u

This should display a prompt that looks like this:

  =====================================================================
  Assignment: Project 1: Hog Ok, version v1.18.1
  =====================================================================

  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Unlocking tests

  At each "? ", type what you would expect the output to be.  Type exit() to quit

  ---------------------------------------------------------------------
  Question 0 > Suite 1 > Case 1
  (cases remaining: 1)

  >>> test_dice = make_test_dice(4, 1, 2)
  >>> test_dice()
  ?

You should type in what you expect the output to be. To do so, you need to first figure out what test_dice will do, based on the description above.

You can exit the unlocker by typing exit().

Typing Ctrl-C on Windows to exit out of the unlocker has been known to cause problems, so avoid doing so.

Problem 1 (2 pt)

Implement the roll_dice function in hog.py. It takes two arguments: a positive integer called num_rolls giving the number of dice to roll and a dice function. It returns the number of points scored by rolling the dice that number of times in a turn: either the sum of the outcomes or 1 (Sow Sad).

  • Sow Sad. If any of the dice outcomes is a 1, the current player's score for the turn is 1.
  • Example 1: The current player rolls 7 dice, 5 of which are 1's. They score 1 point for the turn.
  • Example 2: The current player rolls 4 dice, all of which are 3's. Since Sow Sad did not occur, they score 12 points for the turn.

To obtain a single outcome of a dice roll, call dice(). You should call dice() exactly num_rolls times in the body of roll_dice.

Remember to call dice() exactly num_rolls times even if Sow Sad happens in the middle of rolling. By doing so, you will correctly simulate rolling all the dice together (and the user interface will work correctly).

Note: The roll_dice function, and many other functions throughout the project, makes use of default argument values—you can see this in the function heading:

def roll_dice(num_rolls, dice=six_sided): ...

The argument dice=six_sided means that when roll_dice is called, the dice argument is optional. If no value for dice is provided, then six_sided is used by default.

For example, calling roll_dice(3, four_sided), or equivalently roll_dice(3, dice=four_sided), simulates rolling 3 four-sided dice, while calling roll_dice(3) simulates rolling 3 six-sided dice.

Understand the problem:

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 01 -u

Note: You will not be able to test your code using ok until you unlock the test cases for the corresponding question.

Write code and check your work:

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 01

Check out the Debugging Guide!

Debugging Tips

If the tests don't pass, it's time to debug. You can observe the behavior of your function using Python directly. First, start the Python interpreter and load the hog.py file.

python3 -i hog.py

Then, you can call your roll_dice function on any number of dice you want. The roll_dice function has a default argument value for dice that is a random six-sided dice function. Therefore, the following call to roll_dice simulates rolling four fair six-sided dice.

>>> roll_dice(4)

You will find that the previous expression may have a different result each time you call it, since it is simulating random dice rolls. You can also use test dice that fix the outcomes of the dice in advance. For example, rolling twice when you know that the dice will come up 3 and 4 should give a total outcome of 7.

>>> fixed_dice = make_test_dice(3, 4) roll_dice(2, fixed_dice)
7

On most systems, you can evaluate the same expression again by pressing the up arrow, then pressing enter or return. To evaluate earlier commands, press the up arrow repeatedly.

If you find a problem, you first need to change your hog.py file to fix the problem, and save the file. Then, to check whether your fix works, you'll have to quit the Python interpreter by either using exit() or Ctrl^D, and re-run the interpreter to test the changes you made. Pressing the up arrow in both the terminal and the Python interpreter should give you access to your previous expressions, even after restarting Python.

[default argument value]: http://composingprograms.com/pages/14-designing-functions.html#default-argument-values

Continue debugging your code and running the ok tests until they all pass.

One more debugging tip: to start the interactive interpreter automatically upon failing an ok test, use -i. For example, python3 ok -q 01 -i will run the tests for question 1, then start an interactive interpreter with hog.py loaded if a test fails.

Problem 2 (2 pt)

Implement tail_points, which takes the player's opponent's current score opponent_score, and returns the number of points scored by Pig Tail when the player rolls 0 dice.

  • Pig Tail. A player who chooses to roll zero dice scores 2 * abs(tens - ones) + 1 points; where tens, ones are the tens and ones digits of the opponent's score. The ones digit refers to the rightmost digit and the tens digit refers to the second-rightmost digit.
  • Example 1:

    • The opponent has 46 points, and the current player chooses to roll zero dice. 2 * abs(4 - 6) + 1 = 5, so the player gains 5 points.
  • Example 2:

    • The opponent has 73 points, and the current player chooses to roll zero dice. 2 * abs(7 - 3) + 1 = 9.

Don't assume that scores are below 100. Write your tail_points function so that it works correctly for any non-negative score.

Important: Your implementation should not use str, lists, or contain square brackets [ ]. The test cases will check if those have been used.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 02 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 02

You can also test tail_points interactively by running python3 -i hog.py from the terminal and calling tail_points on various inputs.

Problem 3 (2 pt)

Implement the take_turn function, which returns the number of points scored for a turn by rolling the given dice num_rolls times.

Your implementation of take_turn should call both roll_dice and tail_points rather than repeating their implementations.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 03 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 03


Problem 4 (1 pt)

Add functions perfect_square and next_perfect_square so that square_update returns a player's total score after they roll num_rolls. You do not need to edit the body of square_update.

  • Square Swine. After a player gains points for their turn, if the resulting score is a perfect square, then increase their score to the next higher perfect square. A perfect square is any integer n where n = d * d for some integer d.
  • Example 1:

    • A player has 12 points and rolls 3 dice that total 13 points. Their new score would be 25, but since 25 is 5 squared, their score is increased to 6 squared: 36.
  • Example 2:

    • A player has 12 points and rolls 3 dice that total 12 point. Their new score would be 24, which is not a perfect square.
  • Example 3:

    • A player has 0 points and rolls 5 dice, but one is a 1, so their new score would be 1. 1 is a perfect square, and so their score is increased to 4.
  • Example 4:

    • A player has 80 points and rolls 10 dice, but three are 1's, so their new score would be 1. 81 is 9 squared, so their new score is 10 squared: 100. They win the game.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 04 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 04

Problem 5 (5 pt)

Implement the play function, which simulates a full game of Hog. Players take turns rolling dice until one of the players reaches the goal score, and the final scores of both players are returned by the function.

To determine how many dice are rolled each turn, call the current player's strategy function (Player 0 uses strategy0 and Player 1 uses strategy1). A strategy is a function that, given a player's score and their opponent's score, returns the number of dice that the current player will roll in the turn. An example strategy is always_roll_5 which appears above play.

To determine the updated score for a player after they take a turn, call the update function. An update function takes the number of dice to roll, the current player's score, the opponent's score, and the dice function used to simulate rolling dice. It returns the updated score of the current player after they take their turn. Two examples of update functions are simple_update andsquare_update.

If a player achieves the goal score by the end of their turn, i.e. after all applicable rules have been applied, the game ends. play will then return the final total scores of both players, with Player 0's score first and Player 1's score second.

Some example calls to play are:

  • play(always_roll_5, always_roll_5, simple_update) simulates two players that both always roll 5 dice each turn, playing with just the Sow Sad and Pig Tail rules.
  • play(always_roll_5, always_roll_5, square_update) simulates two players that both always roll 5 dice each turn, playing with the Square Swine rule in addition to the Sow Sad and Pig Tail rules (i.e. all the rules).

Important: For the user interface to work, a strategy function should be called only once per turn. Only call strategy0 when it is Player 0's turn and only call strategy1 when it is Player 1's turn.

Hints:

  • If who is the current player, the next player is 1 - who.
  • To call play(always_roll_5, always_roll_5, square_update) and print out what happens each turn, run python3 hog_ui.py from the terminal.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 05 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 05

Check to make sure that you completed all the problems in Phase 1:

python3 ok --score

Then, submit your work to Gradescope before the checkpoint deadline:

When you run ok commands, you'll still see that some tests are locked because you haven't completed the whole project yet. You'll get full credit for the checkpoint if you complete all the problems up to this point.

Congratulations! You have finished Phase 1 of this project!


Interlude: User Interfaces

There are no required problems in this section of the project, just some examples for you to read and understand. See Phase 2 for the remaining project problems.

Printing Game Events

We have built a simulator for the game, but haven't added any code to describe how the game events should be displayed to a person. Therefore, we've built a computer game that no one can play. (Lame!)

However, the simulator is expressed in terms of small functions, and we can replace each function by a version that prints out what happens when it is called. Using higher-order functions, we can do so without changing much of our original code. An example appears in hog_ui.py, which you are encouraged to read.

The play_and_print function calls the same play function just implemented, but using:

  • new strategy functions (e.g., printing_strategy(0, always_roll_5)) that print out the scores and number of dice rolled.
  • a new update function (square_update_and_print) that prints the outcome of each turn.
  • a new dice function (printing_dice(six_sided)) that prints the outcome of rolling the dice.

Notice how much of the original simulator code can be reused.

Running python3 hog_ui.py from the terminal calls play_and_print(always_roll_5, always_roll_5).

Accepting User Input

The built-in input function waits for the user to type a line of text and then returns that text as a string. The built-in int function can take a string containing the digits of an integer and return that integer.

The interactive_strategy function returns a strategy that let's a person choose how many dice to roll each turn by calling input.

With this strategy, we can finally play a game using our play function:

Running python3 hog_ui.py -n 1 from the terminal calls play_and_print(interactive_strategy(0), always_roll_5), which plays a game betweem a human (Player 0) and a computer strategy that always rolls 5.

Running python3 hog_ui.py -n 2 from the terminal calls play_and_print(interactive_strategy(0), interactive_strategy(1)), which plays a game between two human players.

You are welcome to change hog_ui.py in any way you want, for example to use different strategies than always_roll_5.

Graphical User Interface (GUI)

We have also provided a web-based graphical user interface for the game using a similar approach as hog_ui.py called hog_gui.py. You can run it from the terminal:

python3 hog_gui.py

Like hog_ui.py, the GUI relies on your simulator implementation, so if you have any bugs in your code, they will be reflected in the GUI. This means you can also use the GUI as a debugging tool; however, it's better to run the tests first.

The source code for the Hog GUI is publicly available on Github but involves several other programming languages: Javascript, HTML, and CSS.


Phase 2: Strategies

In this phase, you will experiment with ways to improve upon the basic strategy of always rolling five dice. A strategy is a function that takes two arguments: the current player's score and their opponent's score. It returns the number of dice the player will roll, which can be from 0 to 10 (inclusive).

Problem 6 (2 pt)

Implement always_roll, a higher-order function that takes a number of dice n and returns a strategy that always rolls n dice. Thus, always_roll(5) would be equivalent to always_roll_5.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 06 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 06

Problem 7 (2 pt)

A strategy only has a fixed number of possible argument values. In a game to 100, there are 100 possible score values (0-99) and 100 possible opponent_score values (0-99), giving 10,000 possible argument combinations.

Implement is_always_roll, which takes a strategy and returns whether that strategy always rolls the same number of dice for every possible argument combination.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 07 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 07

Problem 8 (2 pt)

Implement make_averaged, which is a higher-order function that takes a function original_function as an argument.

The return value of make_averaged is a function that takes in the same number of arguments as original_function. When we call this returned function on the arguments, it will return the average value of repeatedly calling original_function on the arguments passed in.

Specifically, this function should call original_function a total of total_samples times and return the average of the results of these calls.

Important: To implement this function, you will need to use a new piece of Python syntax. We would like to write a function that accepts an arbitrary number of arguments, and then calls another function using exactly those arguments. Here's how it works.

Instead of listing formal parameters for a function, you can write *args, which represents all of the arguments that get passed into the function. We can then call another function with these same arguments by passing these *args into this other function. For example:

>>> def printed(f):
...     def print_and_return(*args):
...         result = f(*args)
...         print('Result:', result)
...         return result
...     return print_and_return
>>> printed_pow = printed(pow)
>>> printed_pow(2, 8)
Result: 256
256
>>> printed_abs = printed(abs)
>>> printed_abs(-10)
Result: 10
10

Here, we can pass any number of arguments into print_and_return via the *args syntax. We can also use *args inside our print_and_return function to make another function call with the same arguments.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 08 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 08

Problem 9 (2 pt)

Implement max_scoring_num_rolls, which runs an experiment to determine the number of rolls (from 1 to 10) that gives the maximum average score for a turn. Your implementation should use make_averaged and roll_dice.

If two numbers of rolls are tied for the maximum average score, return the lower number. For example, if both 3 and 6 achieve a maximum average score, return 3.

You might find it useful to read the doctest and the example shown in the doctest for this problem before doing the unlocking test.

Important: In order to pass all of our tests, please make sure that you are testing dice rolls starting from 1 going up to 10, rather than from 10 to 1.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 09 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 09

Running Experiments

The provided run_experiments function calls max_scoring_num_rolls(six_sided) and prints the result. You will likely find that rolling 6 dice maximizes the result of roll_dice using six-sided dice.

To call this function and see the result, run hog.py with the -r flag:

python3 hog.py -r

In addition, run_experiments compares various strategies to always_roll(6). You are welcome to change the implementation of run_experiments as you wish. Note that running experiments with tail_strategy and square_strategy will not have accurate results until you implement them in the next two problems.

Some of the experiments may take up to a minute to run. You can always reduce the number of trials in your call to make_averaged to speed up experiments.

Running experiments won't affect your score on the project.


Problem 10 (2 pt)

A strategy can try to take advantage of the Pig Tail rule by rolling 0 when it is most beneficial to do so. Implement tail_strategy, which returns 0 whenever rolling 0 would give at least threshold points and returns num_rolls otherwise. This strategy should not also take into account the Square Swine rule.

Hint: You can use the tail_points function you defined in Problem 2.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 10 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 10

You should find that running python3 hog.py -r now shows a win rate for tail_strategy close to 57%.

Problem 11 (2 pt)

A better strategy will take advantage of both Pig Tail and Square Swine in combination. Even a small number of pig tail points can lead to large gains. For example, if a player has 31 points and their opponent has 42, rolling 0 would bring them to 36 which is a perfect square, and so they would end the turn with 49 points: a gain of 49 - 31 = 18!

The square_strategy returns 0 whenever rolling 0 would result in a score that is at least threshold points more than the player's score at the start of turn.

Hint: You can use the square_update function.

Before writing any code, unlock the tests to verify your understanding of the question:

python3 ok -q 11 -u

Once you are done unlocking, begin implementing your solution. You can check your correctness with:

python3 ok -q 11

You should find that running python3 hog.py -r now shows a win rate for square_strategy close to 62%.

Optional: Problem 12 (0 pt)

Implement final_strategy, which combines these ideas and any other ideas you have to achieve a high win rate against the baseline strategy. Some suggestions:

  • If you know the goal score (by default it is 100), there's no benefit to scoring more than the goal. Check whether you can win by rolling 0, 1 or 2 dice. If you are in the lead, you might decide to take fewer risks.
  • Instead of using a threshold, roll 0 whenever it would give you more points on average than rolling 6.

You can check that your final strategy is valid by running ok.

python3 ok -q 12

Project submission

Run ok on all problems to make sure all tests are unlocked and pass:

python3 ok

You can also check your score on each part of the project:

python3 ok --score

Once you are satisfied, submit this assignment by uploading hog.py to Gradescope. For a refresher on how to do this, refer to Lab 00.

Congratulations, you have reached the end of your first CS 61A project! If you haven't already, relax and enjoy a few games of Hog with a friend.

/proj/hog_contest

Hog Contest

If you're interested, you can take your implementation of Hog one step further by participating in the Hog Contest, where you play your final_strategy against those of other students. The winning strategies will receive extra credit and will be recognized in future semesters!

To see more, read the contest description. Or check out the leaderboard.